Today we will see here the T-V diagram of a pure
substance with the help of this post.

Let us first see here some basic introduction parts
and then we will draw the T-V diagram of a pure substance. Water boils at a
temperature of 1000C. Is it correct? No this is not correct answer
because we have not mentioned the value of pressure here. We will have to say
that water boils at a temperature of 1000C at a pressure of 1 atm.

Let us think that we have increased the value of
pressure and now new pressure is 5 atm, in this situation boiling point of
water will also be increased and it will have some value but will be greater than
1000C. So we will have two important terms here i.e. saturation
temperature and second one is saturation pressure.

If we keep the pressure constant, temperature at
which a pure substance will change its phase will be termed as saturation
temperature. Similarly if we keep the temperature constant, pressure at which a
pure substance will change its phase will be termed as saturation pressure.

Let
us come to the main subject i.e. T-V diagram of pure substance

Let us consider one cylinder piston arrangement as
shown in figure. Let us consider that initially working fluid is water and it is
contained inside the cylinder at a temperature of 200C. Let us
consider that we are providing heat energy to the system at constant pressure.

As we are providing heat energy to the cylinder or
to the system at constant pressure of 1 atm. Therefore temperature of water
will increase and volume or specific volume of water will also increase slightly.
Let we are providing heat energy to the system till water reaches to saturation
temperature at 1 atm pressure i.e. 1000C. Hence we will have one
process 1-2. During this process water is heated at constant pressure of 1 atm
from 200C to 1000C. Finally water will be at saturated
liquid state at point 2 as displayed in figure.

Let us think that we are providing more heat energy
to the system. Now temperature will be constant and boiling of water will be
started. At state 3, as displayed in figure, we will have liquid vapour mixture.
Finally working fluid will reach to point 4, by heating at constant temperature
and constant pressure, where there will not be a single drop of liquid in
working fluid and this point will be termed as saturated vapour state.

Let us think that we are providing more heat energy
to the system. Saturated vapour will now be converted in to super heated steam
and during this process temperature will be increased. Super heated steam is
displayed in figure by a point 5 in above figure.

So we have one curve, between temperature versus
volume for a pure substance (water in this example), and we have displayed this
curve by the process 1-2-3-4-5.

So we have drawn the T-V curve for displaying the
phase change process of water at a pressure of 1 atm. Now in order to secure
the T-V diagram of pure substance, we will have to draw the similar curve for
other pressure values also.

Let we have added weights over the piston in order
to increase the pressure value of the system. Let now system is at pressure of
1 MPa. Now we will see some important points.

T-V
diagram for pure substance

Working fluid i.e. water is now at pressure of 1 MPa,
let us consider that we are providing the heat energy to the system at constant
pressure of 1 MPa. We will again secure one another T-V curve as shown in
figure for pressure of P2, we have taken P2 for the value of pressure 1 MPa . T-V curve for both pressure values will be quite
similar to each other but there will be some differences and we will see these
differences below.

Boiling point of water will be higher now as
compared to that of earlier condition because operating pressure P2 (1 MPa) is
higher in second case as compared to earlier operating pressure of P1(1 atm).

Specific volume or simply volume of saturated liquid
at 1 MPa will be larger as compared to respective value for 1 atm pressure. Similarly,
Specific volume or simply volume of saturated vapour at 1 MPa will be smaller
as compared to respective value for 1 atm pressure.

Constant temperature line displayed by horizontal
line in figure, which connects saturated liquid and saturated vapour states,
will also be smaller as compared to that for 1 atm pressure.

Similarly if we draw the T-V curve for other higher
pressure values, we will have similar other saturation lines or T-V curve but
saturation lines will become shorter as we will go for increasing pressure.

Now we will combine each saturated liquid state
point and we will have one line which will be termed as saturated liquid line.
Similarly, we will combine each saturated vapour state point and we will have
one line which will be termed as saturated vapour line. These two lines i.e. saturated
liquid line and saturated vapour line meet with each other at a point which will be
termed as critical point.

Therefore we can say that critical point will be
defined as a point where saturated liquid state and saturated vapour state are
identical.

Once we have joined the saturation liquid line and
saturated vapour line, we will have one dome type of shape and that is T-V
diagram for a pure substance.

Region left side of the saturated liquid line will
be termed as compressed liquid region and similarly region right side of the
saturated vapour line will be termed as vapour region and these two regions
will be single phase region.

Region falls under the dome will be termed as
saturated liquid-vapour mixture region or simply wet region.

Do you have any suggestions? Please write in comment
box.

We will see another topic in our next post in the
category of thermal engineering.